A dampening unit is provided with a metering roller in printing presses used in printing technology, for example in offset printing, and has the object of transferring a moistening agent film as thinly and uniformly as possible onto the printing block of a printing block cylinder, the print outcome being dependent upon the quality of the supply of moistening agent. In the film dampening units of offset presses, a supplement of isopropyl alcohol of between 8% and 15% is used as a rule in order to ensure perfect dampening. However, since isopropyl alcohol is one of the highly volatile organic solvents which have a disadvantageous effect on the environment efforts are being made world-wide to reduce its emission significantly.